Transition Metal Complexes

Many transition metal complexes are characterized by the presence of an open
shell. Thus an octahedral Ti(III) complex is likely to have one unpaired
electron in the 3d shell of Ti, and have the state 2T2g.
For example, the complex [TiIII(H2O)6]3+
is expected to have a ground state 2Tg, and this is, in fact, correctly
predicted.

Calculation of metal complexes is made difficult for several reasons:

The systems often involve multiple open shells, e.g. high and low spin
complexes. To allow for this, extended C.I. calculations were necessary.

The Jahn-Teller effect predicts that calculated systems should distort so
as to lower the symmetry. To prevent this distortion in systems where the Jahn-Teller
effect is small (the left hand side of the transition metal series), "average
over configurations" was used. This is done automatically if the system
is of high symmetry and the symmetry is conserved by use of symmetry
constraints. In all other cases, the Jahn-Teller effect is allowed to
distort the geometry.

Many textbooks and journal articles incorrectly refer to the next higher
point-group when discussing complexes. Thus hexaquo complexes are
considered as having octahedral symmetry, Oh, instead of the correct Th
symmetry. Because the symmetry analyzer is unaware of this, the symmetry
printed is often in variance with that reported.

In solids, the effect of the next layer of ions is often important.
In the hexahalo complexes, the next layer consists of metal ions, and is
only slightly further away than the halide ions. This effect is always
present in solids where the complex is not electroneutral, e.g. in [MIIIX6]3-
ions in the solid MX3. To allow for this, two special entities are
provided, these have the symbols At (Astatine) and Fr (Francium). The
entity "At" behaves like a point-charge with a charge of -0.5, and "Fr"
behaves like a point-charge with a charge of +0.5. These entities should
only ever be used in even numbers, so that the total charge is an
integer. A more realistic model of the [MIIIX6]3-
system could be constructed by adding eight Fr entities, arrayed at the
vertices of a cube. This would give rise to the complex [MIIIX6M+1/28]+.

The
following table shows the results of PM6 calculations of the ground state of
various high symmetry transition metal complexes. Where the calculated
heat of formation is zero, the calculated state is the same as the state
expected. Where the calculated ΔHf is positive,
the state expected is calculated to be an excited state, and the value is the
energy of that state, in kcal.mol-1, above the calculated
ground state, in other words, it is a measure of the error.

Complex

ΔHf
(Calc.)

Sc(II)(H2O)6 2Tg

Scandium(ii)
hexafluoride 2T2g

Ti(III)(H2O)6 2Tg

Ti(II)(H2O)6 3Tg

Titanium(III)
hexafluoride 2T2g

Titanium(II)
hexafluoride 3T1g

Titanium(II)
hexachloride 3T1g

Titanium(III)
hexachloride 2T2g

V(III)(H2O)6 3Tg

Vanadium(III)
hexafluoride 3T1g

Vanadium(III)
hexachloride 3T1g

Cr(III)(CN)6 4A2g

Cr(IV)(H2O)6 3Tg

Cr(III)(H2O)6 4Ag

Chromium(0)
hexacarbonyl 1A1g

Chromium(III)
hexafluoride 4A2g

Chromium(III)
hexachloride 4A2g

Fe(III)(CN)6 2T2g

Fe(III)(H2O)6 2Tg

Fe(II)(H2O)6 5Tg

Iron(III)
hexafluoride 2T2g

Iron(II)
hexafluoride 1A1g

Iron(III)
hexachloride 6A1g

Iron(II)
hexachloride 5T2g

Ni(II)(H2O)6 3Ag

Nickel(II)
hexafluoride 3A2g

Nickel(II)
hexachloride 3A2g

Zr(III)(H2O)6 2Tg

Zirconium(III)
hexafluoride 2T2g

Zirconium(III)
hexachloride 2T2g

Mo(III)(H2O)6 4Ag

Molybdenum(0)
hexacarbonyl 1A1g

Molybdenum (VI)
hexafluoride 1A1g

Molybdenum (VI)
hexachloride 1A1g

The following table shows the results of PM6 calculations of the energy of
excitation, in kcal.mol-1, from one state to another of
various high symmetry transition metal complexes, and the comparison with the
values observed by experiment..

Complex

Energy of Excitation (kcal/mol)

Exp.

Calc.

Diff.

V(III)(H2O)6 3Tg (F) -> 3Tg

49.32

V(III)(H2O)6 3Tg (F) -> 3Tg (P)

71.47

Vanadium(III) hexafluoride 3T1g -> 1Eg

29.16

Vanadium(III) hexafluoride 3T1g -> 1T2g

29.16

Vanadium(III) hexafluoride 3T1g -> 3T2g

42.31

Vanadium(III) tetrachloride 3A2 -> 3T1 (P)

42.88

Cr(III)(CN)6 4A2g -> 2Eg

35.51

Cr(III)(CN)6 4A2g -> 2T1g

37.36

Cr(III)(CN)6 4A2g -> 2T2g

52.58

Cr(III)(CN)6 4A2g -> 4T1g

93.62

Cr(III)(CN)6 4A2g -> 4T2g

76.33

Chromium(III) hexafluoride 4A2g -> 2Eg

44.87

Chromium(III) hexafluoride 4A2g -> 2T1g

46.88

Chromium(III) hexafluoride 4A2g -> 2T2g

62.88

Chromium(III) hexafluoride 4A2g -> 4T1g(1)

64.89

Chromium(III) hexafluoride 4A2g -> 4T1g(2)

98.14

Mn(II)(H2O)6 6Ag -> 4Ag

72.33

Mn(II)(H2O)6 6Ag -> 4Eg

71.39

Mn(II)(H2O)6 6Ag -> 4Eg (D)

84.91

Mn(II)(H2O)6 6Ag -> 4Tg

54.03

Mn(II)(H2O)6 6Ag -> 4Tg (G)

66.04

Mn(II)(H2O)6 6Ag -> 4Tg (D)

80.05

Ni(II)(H2O)6 3Ag -> 3Tg

24.3

Ni(II)(H2O)6 3Ag -> 3Tg (F)

39.45

Ni(II)(H2O)6 3Ag -> 3Tg (P)

72.33

Nickel(II) hexafluoride 3A2g -> 1Eg

44.14

Nickel(II) hexafluoride 3A2g -> 3T1g

35.82

Nickel(II) hexafluoride 3A2g -> 3T1g

68.07

Nickel(II) hexafluoride 3A2g -> 3T2g

20.73

Zr(III)(H2O)6 2Tg -> 2Ag

40

Zr(III)(H2O)6 2Tg -> 2Eg

30

Zr(III)(H2O)6 2Tg -> 2Tu

40

Transition Metal Complexes

In almost all cases, the crystal field splitting is too small.
This appears to be a fault in the set of approximations used.